Gardner was best known for creating and sustaining interest in recreational mathematics—and by extension, mathematics in general—throughout the latter half of the 20th century, principally through his "Mathematical Games" columns. These appeared for twenty-five years in Scientific American, and his subsequent books collecting them.[10][11]

After the war, Gardner returned to the University of Chicago.[17] He attended graduate school for a year there, but he did not earn an advanced degree.[1]

In 1950 he wrote an article in the Antioch Review entitled "The Hermit Scientist".[18] It was one of Gardner's earliest articles about junk science, and in 1952 a much-expanded version became his first published book: In the Name of Science: An Entertaining Survey of the High Priests and Cultists of Science, Past and Present.

Early career

In the late 1940s, Gardner moved to New York City and became a writer and editor at Humpty Dumpty magazine where for eight years he wrote features and stories for it and several other children's magazines.[19] His paper-folding puzzles at that magazine led to his first work at Scientific American.[20] For many decades, Gardner, his wife Charlotte, and their two sons, Jim and Tom, lived in Hastings-on-Hudson, New York, where he earned his living as a free-lance author, publishing books with several different publishers, and also publishing hundreds of magazine and newspaper articles.[21] Appropriately enough—given his interest in logic and mathematics—they lived on Euclid Avenue. The year 1960 saw the original edition of his best-selling book ever, The Annotated Alice.[22]

Influence

Martin Gardner had a major impact on mathematics in the second half of the 20th century.[25][26] His column was called "Mathematical Games" but it was much more than that.[27][28][29] His writing introduced many readers to real mathematics for the first time in their lives.[30] The column lasted for 25 years and was read avidly by the generation of mathematicians and physicists who grew up in the years 1956 to 1981.[31][32] It was the original inspiration for many of them to become mathematicians or scientists themselves.[33][34][35][36]

Martin Gardner set a new high standard for writing about mathematics.[54][55][56][57][58] In a 2004 interview he said, "I go up to calculus, and beyond that I don’t understand any of the papers that are being written. I consider that that was an advantage for the type of column I was doing because I had to understand what I was writing about, and that enabled me to write in such a way that an average reader could understand what I was saying. If you are writing popularly about math, I think it’s good not to know too much math."[1] And he was fearsomely bright.[59][60] John Horton Conway called him "the most learned man I have ever met."[43]Colm Mulcahy said, "Gardner was without doubt the best friend mathematics ever had."[43] Many people would agree with him.[61][62][63][64]

Mathematical Games column

For over a quarter century Gardner wrote a monthly column on the subject of recreational mathematics for Scientific American. It all began with his free-standing article on hexaflexagons which ran in the December 1956 issue.[45]Flexagons became a bit of a fad and soon people all over New York City were making them. Gerry Piel, the SA publisher at the time, asked Gardner, "Is there enough similar material to this to make a regular feature?" Gardner said he thought so. The January 1957 issue contained his first column, entitled "Mathematical Games".[21] Almost 300 more columns were to follow.[1]

The "Mathematical Games" column became the most popular feature of the magazine and was the first thing that many readers turned to.[65] In September 1977 Scientific American acknowledged the prestige and popularity of Gardner's column by moving it from the back to the very front of the magazine.[66] It ran from 1956 to 1981 with sporadic columns afterwards and was the first introduction of many subjects to a wider audience, notably:[67][68]

Ironically, Gardner had problems learning calculus and never took a mathematics course after high school. While editing Humpty Dumpty's Magazine he constructed many paper folding puzzles, and this led to his interest in the flexagons invented by British mathematician Arthur H Stone. The subsequent article he wrote on hexaflexagons led directly to the column.[21]

Gardner's son Jim once asked him what was his favorite puzzle, and Gardner answered almost immediately: "The monkeys and the coconuts".[69] It had been the subject of his April 1958 Games column and in 2001 he chose to make it the first chapter of his "best of" collection, The Colossal Book of Mathematics.[70]

In the 1980s "Mathematical Games" began to appear only irregularly. Other authors began to share the column, and the June 1986 issue saw the final installment under that title. In 1981, on Gardner's retirement from Scientific American, the column was replaced by Douglas Hofstadter's "Metamagical Themas", a name that is an anagram of "Mathematical Games".

Virtually all of the games columns were collected in book form starting in 1959 with The Scientific American Book of Mathematical Puzzles & Diversions.[71] Over the next four decades fourteen more books followed. Donald Knuth called them the canonical books.[72][73]

Pseudoscience and skepticism

Martin Gardner is the single brightest beacon defending rationality and good science against the mysticism and anti-intellectualism that surround us.[23]

Gardner was a relentless critic of self-proclaimed Israeli psychicUri Geller and wrote two satirical booklets about him in the 1970s using the pen name "Uriah Fuller" in which he explained how such purported psychics do their seemingly impossible feats such as mentally bending spoons and reading minds.[78]

Skeptical Inquirer named him one of the Ten Outstanding Skeptics of the Twentieth Century.[80] In 2010 he was posthumously honored with an award for his contributions in the skeptical field from the Independent Investigations Group.[81] In 1982 the Committee for Skeptical Inquiry awarded Gardner its In Praise of Reason Award for his "heroic efforts in defense of reason and the dignity of the skeptical attitude",[82] and in 2011 it added Gardner to its Pantheon of Skeptics.[83]

Magic

Card magic, and magic in general, owe a far greater debt to Martin Gardner than most conjurors realize.[84]

–Stephen Minch

Martin Gardner's father once showed him a magic trick when he was a little boy.[85] Young Martin was fascinated to see physical laws seemingly violated and this led to a lifelong passion for magic and illusion. He wrote for a magic magazine in high school and worked in a department store demonstrating magic tricks while he was at the University of Chicago.[86] The very first thing that Martin Gardner ever published (at the age of fifteen) was a magic trick in The Sphinx, the official magazine of the Society of American Magicians.[87] He focused mainly on micromagic (table or close-up magic) and, from the 1930s on, published a significant number of original contributions to this secretive field. Magician Joe M. Turner said, The Encyclopedia of Impromptu Magic, which Gardner wrote in 1985, "is guaranteed to show up in any poll of magicians' favorite magic books."[88][89] His first magic book for the general public, Mathematics, Magic and Mystery (Dover, 1956), is still considered a classic in the field.[87] He was well known for his innovative tapping and spelling effects, with and without playing cards, and was most proud of the effect he called the "Wink Change".[90]

Many of Gardner's lifelong friends were magicians.[91] These included William Simon who introduced Gardner to Charlotte Greenwald, whom he married in 1952, fellow CSICOP founder and pseudoscience fighter James Randi, Dai Vernon, Jerry Andrus, statistician Persi Diaconis, and polymath Raymond Smullyan. Diaconis and Smullyan like Gardner straddled the two worlds of mathematics and magic.[41] Mathematics and magic were frequently intertwined in Gardner's work.[92] One of his earliest books, Mathematics, Magic and Mystery (1956), was about mathematically based magic tricks.[86] Mathematical magic tricks were often featured in his "Mathematical Games" column–for example, his August 1962 column was titled "A variety of diverting tricks collected at a fictitious convention of magicians." From 1998 to 2002 he wrote a monthly column on magic tricks called "Trick of the Month" in The Physics Teacher, a journal published by the American Association of Physics Teachers.[93]

Theism and religion

Gardner believed in a personal God, in an afterlife, and in prayer, but rejected established religion. He considered himself a philosophical theist and a fideist.[95] He had an abiding fascination with religious belief but was critical of organized religion. In his autobiography, he stated: "When many of my fans discovered that I believed in God and even hoped for an afterlife, they were shocked and dismayed... I do not mean the God of the Bible, especially the God of the Old Testament, or any other book that claims to be divinely inspired. For me God is a "Wholly Other" transcendent intelligence, impossible for us to understand. He or she is somehow responsible for our universe and capable of providing, how I have no inkling, an afterlife."[96]

I am a philosophical theist. I believe in a personal God, and I believe in an afterlife, and I believe in prayer, but I don’t believe in any established religion. This is called philosophical theism.... Philosophical theism is entirely emotional. As Kant said, he destroyed pure reason to make room for faith.[95]

– Martin Gardner, 2008

Gardner described his own belief as philosophical theism inspired by the works of philosopher Miguel de Unamuno. While eschewing systematic religious doctrine, he retained a belief in God, asserting that this belief cannot be confirmed or disconfirmed by reason or science.[97] At the same time, he was skeptical of claims that any god has communicated with human beings through spoken or telepathic revelation or through miracles in the natural world.[98] Gardner has been quoted as saying that he regarded parapsychology and other research into the paranormal as tantamount to "tempting God" and seeking "signs and wonders". He stated that while he would expect tests on the efficacy of prayers to be negative, he would not rule out a priori the possibility that as yet unknown paranormal forces may allow prayers to influence the physical world.[99]

Gardner wrote repeatedly about what public figures such as Robert Maynard Hutchins, Mortimer Adler, and William F. Buckley, Jr. believed and whether their beliefs were logically consistent. In some cases, he attacked prominent religious figures such as Mary Baker Eddy on the grounds that their claims are unsupportable. His semi-autobiographical novel The Flight of Peter Fromm depicts a traditionally Protestant Christian man struggling with his faith, examining 20th century scholarship and intellectual movements and ultimately rejecting Christianity while remaining a theist.[97]

Gardner said that he suspected that the fundamental nature of human consciousness may not be knowable or discoverable, unless perhaps a physics more profound than ("underlying") quantum mechanics is some day developed. In this regard, he said, he was an adherent of the "New Mysterianism".[100]

Annotated works

Gardner was considered a leading authority on Lewis Carroll. His annotated version of Alice's Adventures in Wonderland and Through the Looking Glass, explaining the many mathematical riddles, wordplay, and literary references found in the Alice books, was first published as The Annotated Alice (Clarkson Potter, 1960). Sequels were published with new annotations as More Annotated Alice (Random House, 1990), and finally as The Annotated Alice: The Definitive Edition (Norton, 1999), combining notes from the earlier editions and new material. The original book arose when Gardner found the Alice books "sort of frightening" when he was young, but found them fascinating as an adult.[101] He felt that someone ought to annotate them, and suggested to a publisher that Bertrand Russell be asked; when the publisher was unable to get past Russell's secretary, Gardner was asked to take on the project himself.[102]

Novels and short stories

Gardner wrote two novels. He was a perennial fan of the Oz books written by L. Frank Baum,[103] and in 1988 he published Visitors from Oz, based on the characters in Baum's various Oz books. Gardner was a founding member of the International Wizard of Oz Club, and winner of its 1971 L. Frank Baum Memorial Award. His other novel was The Flight of Peter Fromm (1973), which reflected his lifelong fascination with religious belief and the problem of faith.[104]

His short stories were collected in The No-Sided Professor and Other Tales of Fantasy, Humor, Mystery, and Philosophy (1987).[1]

Autobiography

At the age of 95 Gardner wrote Undiluted Hocus-Pocus: The Autobiography of Martin Gardner. He was living in a one-room apartment in Norman, Oklahoma and, as was his custom, wrote it on a typewriter and edited it using scissors and rubber cement.[42] He took the title from a grook by his good friend Piet Hein,[105] a grook which perfectly expresses Gardner's abiding sense of mystery and wonder about existence.

Pen names

Gardner often used pen names. In 1952, while working for the children's magazine Humpty Dumpty, he contributed stories written by "Humpty Dumpty Jnr". For several years starting in 1953 he was a managing editor of Polly Pigtails, a magazine for young girls, and also wrote under that name. His Annotated Casey at the Bat (1967) included a parody of the poem, attributed to "Nitram Rendrag" (his name spelled backwards). Using the pen name "Uriah Fuller", he wrote two books attacking the alleged psychic Uri Geller. In later years, Gardner often wrote parodies of his favorite poems under the name "Armand T. Ringer", an anagram of his name.[108] In 1983 one George Groth panned Gardner's book The Whys of a Philosophical Scrivener in the New York Review of Books. Only in the last line of the review was it revealed that George Groth was Martin Gardner himself.[109]

In his January 1960 Mathematical Games column, Gardner introduced the fictitious "Dr. Matrix" and wrote about him often over the next two decades. Dr. Matrix was not exactly a pen name, although Gardner did pretend that everything in these columns came from the fertile mind of the good doctor. Then in 1979 Dr. Matrix himself published an article in the quite respectable Two-Year College Mathematics Journal.[110] It was called Martin Gardner: Defending the Honor of the Human Mind and contained a biography of Gardner and a history of his Mathematical Games column.[111]

Philosophy of mathematics

Gardner was known for his sometimes controversial philosophy of mathematics.[112] He wrote negative reviews of The Mathematical Experience by Philip J. Davis and Reuben Hersh and What Is Mathematics, Really? by Hersh, both of which were critical of aspects of mathematical Platonism, and the first of which was well received by the mathematical community. While Gardner was often perceived as a hard-core Platonist, his reviews demonstrated some formalist tendencies. Gardner maintained that his views are widespread among mathematicians, but Hersh has countered that in his experience as a professional mathematician and speaker, this is not the case.[113]

Gathering 4 Gardner

Martin Gardner continued to write up until his death in 2010, and his community of fans grew to span several generations.[23] Moreover, his influence was so broad that many of his fans had little or no contact with each other. This led Atlanta entrepreneur and puzzle collector Tom Rodgers to the idea of hosting a weekend gathering celebrating Gardner's contributions to recreational mathematics, rationality, magic, puzzles, literature, and philosophy.[43] Although Gardner was famously shy, and would usually decline an honor if it required him to make a personal appearance, Rogers persuaded him to attend the first such "Gathering 4 Gardner" (G4G), held in Atlanta in January 1993.[121]

A second such get-together was held in 1996, again with Gardner in attendance, and this led Rodgers and his friends to make the gathering a regular, bi-annual event. Participants over the years have ranged from long-time Gardner friends such as Conway, Elwyn Berlekamp, Ronald Graham, Donald Coxeter, and Richard Guy, to newcomers like mathematician and mathematical artist Erik Demaine and mathematical video maker Vi Hart.[23]

The program at the "G4G" meetings presents topics which Gardner had written about. The first gathering in 1993 was G4G1 and the 1996 event was G4G2. Since then it has been in even-numbered years, so far always in Atlanta.[122] The 2018 event was G4G13.[123]

^Bellos (2010): "He became a kind of father figure to a generation of young mathematicians, who corresponded with him. Such was Gardner's influence between the late 1950s and 1980s that it would be hard to find a professional mathematician from those years who does not cite him as an inspiration."

^Princeton University Press: Reviews of Undiluted Hocus-Pocus: "Martin Gardner occupies a special place in twentieth-century mathematics. More than any other single individual, he inspired a generation of young people to study math."–Barry Cipra

^Bellos (2010): He was not a mathematician – he never even took a maths class after high school—yet Martin Gardner, who has died aged 95, was arguably the most influential and inspirational figure in mathematics in the second half of the last century.

^Hofstadter (2010): The word games, with its lightweight flavor, did not even hint at the depth of the issues that the column dealt with.

^Richards (2014): Gardner’s columns seeded scores of new findings—far too many to list.

^Hofstadter (2010): Many of today's most influential mathematicians and physicists, magicians and philosophers, writers and computer scientists, owe their direction to Martin Gardner. They may not even be aware of how big a role he played in their development.

^Mulcahy (Jan 2014): It’s been said that he had a million readers there at his peak.

^Malkevitch (2014): Martin Gardner's columns and books have been referenced by huge numbers of research papers that involve mathematics.

^Antonick (2014): Martin Gardner was well known for inspiring generations of students to become professional mathematicians.

^Antonick (2014): "Martin Gardner’s column in Scientific American was one of the two things that, above all others, convinced me I wanted to be a mathematician."–Ian Stewart

^Demaine (2008) p. ix: Many of today's mathematicians entered this field through Gardner's influence.

^Martin Gardner—Mathematician (official website): "Gardner will go down in history as one of the most significant mathematicians of all time."–Michael Aschbacher, editor of The Journal of Recreational Mathematics

^Knuth (2011): Already when he began his monthly series in 1956 and 1957, he was corresponding with the likes of Claude Shannon, John Nash, John Milnor, and David Gale. Later he would receive mail from budding mathematicians John Conway, Persi Diaconis, Jeffrey Shallit, Ron Rivest, et al.

^Mulcahy (Jan 2014): The surrealist artist was intrigued by Martin’s writings on the 4-dimensional cube, or tesseract—-which had been a prominent feature of his own 1954 painting Crucifixion (Corpus Hypercubus).

^Mulcahy (Oct 2014): It went a lot further than puzzles—there was substance, depth and a fair share of mystery and wonder in the topics he wrote about.

^Mulcahy (Oct 2014): Penrose tiles are a good example of just how 'nontrivial' the consequences of his puzzle column could be. The materials scientist Dan Shechtman actually won a Nobel Prize in chemistry in 2011 'for the discovery of quasicrystals'—three-dimensional Penrose tiles—in some aluminium-manganese alloys.

^Hofstadter (2010): His approach and his ways of combining ideas are truly unique and truly creative, and, if I dare say so, what Martin Gardner has done is of far greater originality than work that has won many people Nobel Prizes.

^Malkevitch (2014): The range of wonderful problems, examples, and theorems that Gardner treated over the years is enormous. They include ideas from geometry, algebra, number theory, graph theory, topology, and knot theory, to name but a few.

^Bellos, Alex (2010): I discovered how good [the columns] really were, covering everything from public-key cryptography to superstring theory. He was the first to cover so many breakthroughs.

^Kullman (1997): "Martin Gardner, in his "Mathematical Games" column in Scientific American presented "for the first time" a description of the Penrose tiles, including many of Conway's results concerning them."

^Jackson (2004): His crystalline prose, always enlightening, never pedantic, set a new standard for high quality mathematical popularization.

^Lister (1995): Martin Gardner's supreme achievement was his ability to communicate difficult and often profound subjects with a few deft, but human strokes of his pen.

^Mirsky (2010): "His writing has been valued by generations of professional mathematicians."–Ian Stewart

^Teller (2014): "Gardner writes with authority and ease. You trust him to take you wherever he feels like going."

^Princeton University Press: Reviews of Undiluted Hocus-Pocus: James Randi called him "a huge intellect."

^Martin (2010): "Martin Gardner is one of the great intellects produced in this country in the 20th century."–Douglas Hofstadter

^Malkevitch (2014): One of the greatest expositors of mathematics, for me perhaps the greatest, was Martin Gardner. Perhaps no one has done more to make the world aware of mathematics than Martin Gardner

^The Economist (2010): His gift, or rather one of them, was to explain mathematical concepts in ways that made sense to non-mathematicians. Many of them not only understood what he wrote but also became infected with his love of maths, of its beauty and of its capacity to give satisfaction.

^Jackson (2004): He opened the eyes of the general public to the beauty and fascination of mathematics and inspired many to go on to make the subject their life’s work.

^Knuth (2011): Indeed, more people have probably learned more good mathematical ideas from Martin Gardner than from any other person in the history of the world.

^Hofstadter (2010): There were thousands of such people spread all around the world—mathematicians, physicists, philosophers, computer scientists, and on and on—who thought of Martin Gardner's column not as merely a feature of that great magazine Scientific American, but as its very heart and soul.

^Adamatzky, A. (Ed.) (2010). Game of Life Cellular Automata ebook, ISBN1849962170. pp. 15-16, Conway came to New York to meet with Gardner [and] could not believe the amount of interest Gardner’s columns on the game of Life had generated.

^Gould (1982): In this climate, beleaguered rationalism needs its skilled debaters—writers who can combine wit, penetrating analysis, sharp prose, and sweet reason into an expansive view that expunges nonsense without stifling innovation, and that presents the excitement and humanity of science in a positive way. ...For more than thirty years, Martin Gardner has played this largely thankless role with tireless efficiency. He is more than a mere individual fighting a set of personal battles; he has become a priceless national resource.

^MacTutor: My mother read The Wizard of Oz to me when I was a little boy, and I looked over her shoulder as she read it. I learned how to read that way.

^Brown (2010): Faith was also the subject of his 1973 semi-autobiographical novel, "The Flight of Peter Fromm," in which the title character and his atheist professor of divinity grapple for decades with questions about God.